While the informal form in the examples above is used by people who are of the same age and/or close, or when older people are talking to younger people in informal situations, thepolite form is commonly used by younger people addressing older people, and in any formal situations.

Formal

Can do

Could do

Written

할 수 있습니다

할 수 있었습니다

Spoken

할 수 있어요

할 수 있었어요

Formal

Can't do

Couldn't do

Written

할 수 없습니다
못 합니다

할 수 없었습니다
못 했습니다

Spoken

할 수 없어요

못 해요

할 수 없었어요

못 했어요

Note: The ones in bold characters are more commonly used alternative of the two in each box.

I understand this grammar pattern, but then I found a sentence that used ㄹ 수가 없다 instead of plain ㄹ 수 없다. It was also translated as "can't do X." Is adding the 가 a formality or does it make it sound more poetic? I would appreciate any sort of help!